Chapter 20 Magnetism

MagnetsThe ends of a bar magnet are called poles

Like poles repel and unlike poles attractRegardless of their shape, all magnets have

a north and south pole

Magnetic FieldsMagnetic Field lines point from the north pole

to the south pole of the magnetThe north pole of a compass needle always

points in the direction of the field (from North to South)

Magnetic Field of the EarthThe Earth’s geographic North pole is

actually the magnetic south poleThe north pole of a compass points towards

geographic north and since opposites attract, we know that the Earth’s geographic pole is magnetic south

Magnetic Force A charge moving through a magnetic field

experiences a force

q= magnitude of chargev= speed of chargeB= Strength of the magnetic field (measured in

Tesla, T)θ= angle between v and B (F=0 if θ=0)

sinqvBFmagnetic

A second Right-Hand RuleOf course, force is a vector!

To find the direction of the magnetic force use another right hand ruleFingers point in direction of the fieldThumb points in direction of vPalm points in direction of magnetic force

Conventions for direction of fieldDirection of Field

Symbol

Into the page

X

Out of the page

WARNING: The right hand rule is for thedirection of the force acting on a POSITIVE CHARGE.

To find the direction of the force acting on a negative charge, you’ll have to use the rule and change the sign!

ExamplesDirection of F Direction of v Direction of B Sign of Charge

Out of the page East North +

Into the page East North -

Out of the page West South +

Into the page West South -

South West Into the page +

South West Out of the page -

East North Out of the page +

South Out of the page East -

Out of the page South West -

Into the page west North +

Path of a charge in a magnetic fieldThe path of a charged particle moving

perpendicular to a magnetic field is a circle (p.595)

The magnetic force acting on the particle acts like the centripetal force

r

mvqvBFmagnetic

2

Magnetic Field of a wireMoving charges produce

magnetic fieldsIf there is a current

moving through a wire, a magnetic field is produced around the wire

I is current, r is perpendicular to wire

µo=4π x 10-7 Tm/A

r

IB o

2

Magnetic Field of a wireThe “Right Hand Rule” for the magnetic

field

Point your thumb in the direction of the current and curl your fingers in the direction of the field

Force on a current carrying wireA magnet exerts a force on a current-carrying

wire

I= currentl= length of wireB= magnitude of magnetic fieldΘ is the angle between the direction of current

and the magnetic fieldIf current is parallel to B, F=0 (F=0 if θ=0)

sinIlBFmagnetic

The Right-Hand Rule revisedOf course, force is a vector!

To find the direction of the magnetic force use another right hand ruleFingers point in direction of the fieldThumb points in direction of I Palm points in direction of magnetic force

I

Force between two current carrying wires

Two current-carrying wires exert a force on each otherIf the currents are moving in the same direction the

wires attract each otherIf the currents are moving in opposite directions, the

wires repel

2.0x10-7 Tm/A= µo/2πI= currentl= length of wireL= distance between wires

L

lIIATm

x

L

lIIF o

217

21

100.2

2

Electromagnetic Induction (Ch 20)Michael Faraday

discovered the phenomenon of electromagnetic induction

A changing magnetic field can produce an electric current (induced current)B must be changing

for this to work

Moving a magnet through a coil of wire produces acurrent

Magnetic FluxMagnetic Flux is proportional to the

number of field lines passing through some area

The angle θ is the angle between B and a line drawn perpendicular to the surface

If θ is 90, no lines pass through the area, so flux is 0

Unit for flux is the Weber (1Wb= 1 Tm2 )

BAcosθΦFlux Magnetic B

Faraday’s Law of InductionRecall what electromagnetic induction is. A

changing magnetic field induces a current

Faraday’s Law mathematically:

N represents the number of loops in the wireΔΦB is the change in magnetic flux

t

BN(Voltage) Emf Induced

Lenz’s Law

The negative sign indicates that the induced current’s magnetic field is always opposite to the original change in fluxChanging flux induces an emf, which induces a

currentThat current then produces its own magnetic

fieldThat magnetic field points in the opposite

direction of the change in flux

t

BN(Voltage) Emf Induced

Lenz’s Law

Direction of the magnetic field produced by the induced current?A. DownB. Up

More Practice with Lenz’s Law

b. The area decreases, so flux decreases. Current will be clockwise to produceA field that points into the page

a. Current produced will be counterclockwise to produce a field that points outof the page

In which direction is the current induced in the coil for each situation?

c. Initially flux is out of the page. Moving the coil means the flux decreases.Induced current will be counterclockwise to produce a field out of the pge

d. Field lines and surface are parallel so there is no flux, so no current is induced

e. Flux will increase to the left so the current will be counterclockwise to produce a Field to the right

Induced EMF for moving conductorWhat if the magnet is stationary and the

wire is moved instead?This is called motional emf

B= magnetic fieldl= length of wirev= speed

Blv(Voltage) Emf Induced

Sample Problem p. 655 #15B= 0.450 TR= 0.230 Ωv= 3.40 m/s

Calculate the force required to pull the loop from the field at a constant velocity of 3.4 m/s

How do we get force?

We have l, B what’s I?Ohm’s Law I= V/R.

We have R…what’s V??Law of induction!:V=Blv=0.5355 VI=V/R=0.5355V/0.230 Ω= 2.33 AF=IlB= (2.33A)(0.350m)(0.450 T)= 0.367 N

IlBFmagnetic

Blv(Voltage) Emf Induced